Robust classification with flexible discriminant analysis in heterogeneous data

TL;DR

This paper introduces a robust discriminant analysis method that models each data point with its own elliptical distribution and scale, enabling effective classification in heterogeneous, non-Gaussian datasets.

Contribution

It proposes a novel flexible discriminant analysis framework that handles heterogeneity and non-Gaussianity by allowing individual elliptical distributions for data points.

Findings

Simple and fast maximum-likelihood estimation

Enhanced robustness to non-Gaussian and contaminated data

Effective classification in heterogeneous datasets

Abstract

Linear and Quadratic Discriminant Analysis are well-known classical methods but can heavily suffer from non-Gaussian distributions and/or contaminated datasets, mainly because of the underlying Gaussian assumption that is not robust. To fill this gap, this paper presents a new robust discriminant analysis where each data point is drawn by its own arbitrary Elliptically Symmetrical (ES) distribution and its own arbitrary scale parameter. Such a model allows for possibly very heterogeneous, independent but non-identically distributed samples. After deriving a new decision rule, it is shown that maximum-likelihood parameter estimation and classification are very simple, fast and robust compared to state-of-the-art methods.